Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Graeffe's, Chebyshev-like, and Cardinal's processes for splitting a polynomial into factors
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Matrix computations (3rd ed.)
A unifying convergence analysis of second-order methods for secular equations
Mathematics of Computation
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
On the geometry of Graeffe Iteration
Journal of Complexity
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
An iterated eigenvalue algorithm for approximating roots of univariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
SIAM Journal on Matrix Analysis and Applications
Schur aggregation for linear systems and determinants
Theoretical Computer Science
Experimental evaluation and cross-benchmarking of univariate real solvers
Proceedings of the 2009 conference on Symbolic numeric computation
The amended DSeSC power method for polynomial root-finding
Computers & Mathematics with Applications
Additive preconditioning for matrix computations
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
New progress in real and complex polynomial root-finding
Computers & Mathematics with Applications
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Recent progress on root-finding for polynomial and secular equations largely relied on eigen-solving for the associated companion and diagonal plus rank-one generalized companion matrices. By applying to them Rayleigh quotient iteration, we could have already competed with the current best polynomial root-finders, but we achieve further speedup by applying additive preprocessing. Moreover our novel rational maps of the input matrix enables us to direct the iteration to approximating only real roots, so that we dramatically accelerate their numerical computation in the important case where they are much less numerous than all complex roots.